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A197629
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Number of ways to write n as the sum of two coprime, squarefree, composite, positive integers.
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3
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 5, 0, 0, 0, 1, 0, 3, 1, 2, 0, 3, 0, 4, 1, 0, 1, 3, 0, 5, 0, 2, 0, 4, 0, 1, 2
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OFFSET
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1,41
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LINKS
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EXAMPLE
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a(29) is the first nonzero term since 29=15+14. The first nonzero even term is a(68) since 68=3(11)+5(7). Then the first even term with a value greater than one is a(86) since 86=3(7)+5(13) and 86=5(7)+3(17).
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PROG
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(MATLAB)
function [asubn]=ccsf(n)
% ccsf(n) returns the n-th term of the sequence of composite, coprime, square
% free sums of the integer n
r=0;
k=6;
while k<n/2,
if isprime(k)+isprime(n-k) == 0
if gcd(k, n-k) == 1
if prod(diff(factor(k)))*prod(diff(factor(n-k)))>0
r = r+1;
end
end
end
k=k+1;
end
asubn=r;
end
(PARI) a(n)=sum(k=4, (n-1)\2, gcd(k, n-k)==1&&!isprime(k)&&!isprime(n-k)&&issquarefree(k)&&issquarefree(n-k)) \\ Charles R Greathouse IV, Oct 18 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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